As a local, here's the answer:
Dallas Cowboys
Dallas Mavericks
Texas Rangers
Texas Longhorns
Oklahoma Sooners
Dallas Stars
FC Dallas
Pretty accurate. Personally, I'd bump the Horns up to #2 or at least tied with the Mavs, but's that's about all I'd change. I want to believe the Stars are more popular than OU, but probably not.
Football is the biggest sport here in TX, always has been and always will be. The Cowboys have had success that most of us are old enough to remember, and usually have a decent team. UT has a storied history. TCU just made it to a National Championship. There's high school stadiums here bigger than college stadiums in northern states. So football will just always be #1. The Dallas Cowboys are the most valuable sports franchise in the world at $8 billion.
Baseball has a long history in TX and as "America's Pastime", it has always enjoyed immense popularity. The Rangers are terrible, but have had some recent success. They just got a new air conditioned stadium and you can easily get pretty cheap seats to Rangers games. Again, college and high school baseball are both incredibly popular here.
Basketball has been pretty popular in Texas for decades. All three Texas teams (Dallas, Houston, and San Antonio) have had maintained success over the past 20+ years and have won championships. Luka Doncic is arguably the best player in the league and looks like he will have an incredible HOF career. Like football and baseball, college and high school basketball is a huge draw. There's courts everywhere.
Hockey is totally different. Yes the Stars have had some recent success, but were terrible before that. Hockey teams at the collegiate and especially high school level are extremely rare. You're more likely to see lacrosse. That's just a function of the cost of entry of the sport and few rinks. I love hockey and think that the ticket prices aren't bad for what the product is, but it's not as cheap as going to Rangers or Mavs games. I don't know how much of a bump the team has seen due to recent playoff runs, but I'd surmise that the gap between the Big 3 and hockey here is enormous.
Dallas Stars fans are plentiful enough to fill the seats every game. In a metroplex of a million people, you can only sell 20k tickets, so there's definitely enough fans. I'd say that on average, they seem pretty dedicated. I'd be curious to see what percentage of seats are held by season ticket holders and how that compares league wide. Perhaps if they won a Cup, the following season could see them close the gap a little bit, but I doubt that would be enough. In order for the Stars to move up in the rankings here, every other team would need to be complete garbage at the exact same time that the Stars had a dynasty.
I think all of this is probably true for every NHL city. Going back to 1999 just to include the Stars, here's the list of Cup winners. In any of these cases were they ever the most popular team in the city? Were they even second?
Colorado Avalanche
Tampa Bay Lightning
St. Louis Blues
Washington Capitals
Pittsburgh Penguins
Chicago Blackhawks
Los Angeles Kings
Boston Bruins
Detroit Red Wings
Anaheim Ducks
Carolina Hurricanes
New Jersey Devils
Dallas Stars
Looking at that list, I'm not sure if any of those teams were ever higher than #3.